Unfortunately if you were in an at fault single car accident without having insurance (specifically physical damage insurance coverage) on your car then you would not have any coverage to take care of the damages to your car. If the cost of repairs is more than what the car is worth then it would be termed to be a total loss.

You said you still owe on the vehicle, which normally means that the lien holder requires you to carry not only the minimum state liability limits but also comprehensive and collision. If you did not have this coverage on your vehicle the lien holder may have taken out "forced insurance" on the vehicle. You would need to check with the financial institute which your loan is through to find out if this was on the car at the time of the accident and if so if it would help you in any way.

As for your GAP insurance, it normally only comes into play after your primary insurer has paid out for the total loss of your vehicle. If you were without a primary insurance provider at the time of the accident then there is no one to pay the actual cash value of the vehicle. Without the payout of the ACV for the vehicle, GAP insurance usually also does not pay out since it is there to pay the difference between ACV and the balance of your loan not the entire loan amount.

You can contact your Gap insurance carrier to find out for certain if they will allow you to make a claim. If a claim is allowed then it would be placed on your claims history or claims record. As for your driving record, accidents are usually placed on here by the police that take a report of the accident and not insurance companies.